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- Title
Nordhaus–Gaddum-Type Results for the Steiner Gutman Index of Graphs.
- Authors
Wang, Zhao; Mao, Yaping; Das, Kinkar Chandra; Shang, Yilun
- Abstract
Building upon the notion of the Gutman index SGut (G) , Mao and Das recently introduced the Steiner Gutman index by incorporating Steiner distance for a connected graph G. The Steiner Gutman k-index SGut k (G) of G is defined by SGut k (G) = ∑ S ⊆ V (G) , | S | = k ∏ v ∈ S d e g G (v) d G (S) , in which d G (S) is the Steiner distance of S and d e g G (v) is the degree of v in G. In this paper, we derive new sharp upper and lower bounds on SGut k , and then investigate the Nordhaus-Gaddum-type results for the parameter SGut k . We obtain sharp upper and lower bounds of SGut k (G) + SGut k (G ¯) and SGut k (G) · SGut k (G ¯) for a connected graph G of order n, m edges, maximum degree Δ and minimum degree δ.
- Subjects
GRAPH connectivity
- Publication
Symmetry (20738994), 2020, Vol 12, Issue 10, p1711
- ISSN
2073-8994
- Publication type
Article
- DOI
10.3390/sym12101711